Cat attacked by dog "No one can Help"

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There is a friendly stray cat here in my neighborhood that comes by to visit me quite often. Well last night it was attacked by a dog outside my complex and I tried to find it and couldn't until this afternoon. I found her injured and curled up under some stairs barely able to move. I have a family of 6 and barely scrape by as it is but still I called every vet in town trying to find out how to get her care. I can afford the initial $50 for being seen (well I can't but I'd get it) but tried to find a place that would take payments on the remaining balance if there was one and not one single place offers a discount or payments of any kind. The best I could get was take it to the Humane Society and sign a paper to relinquish rights if it was mine. But you know what the H.S. here is unable to care for injured animals they told me they are typically euthanized right away because they can not afford it. I am so irritated right now. How is this cat suppose to get help and survive if I can not find anyone to take care of her... For all these places that are suppose to have a deep love for animals you'd think there would be at least one option. But they would rather let her die then risk setting up payments.